Model-based infusion site monitor

ABSTRACT

A medication delivery monitoring device is disclosed. The device includes a user interface configured to receive input information, and a sensor configured to measure a plurality of fluid state parameters of a fluid delivery channel through which the medication is delivered by a vascular access device (VAD) to an infusion site region of the patient. The device also includes a processor configured to determine a state of the infusion site region based on the plurality of measured fluid state parameters and the input information, and an output device configured to provide a communication regarding the state of the infusion site region. Methods and computer-readable mediums for monitoring medication delivery are also disclosed.

TECHNICAL FIELD

The present disclosure generally relates to management of infusionmedications, and more particularly, to a system for detectingabnormalities in the flow of infusion medications to a patter.

DESCRIPTION OF THE RELATED ART

Many individuals suffer from chronic health problems, the treatment ofwhich requires regular, and sometimes extended, intravenous medicationdeliveries. Certain treatment regimens for diseases such as diabetes,asthma, epilepsy, cancer and even allergies, require the regular undsequenced infusion of precise amounts of intravenous medication fur thepatient's survival. Intravenous infusion of medications can take on manyforms depending on the patient, treatment regimen, and choices of theclinician and institution. Many infusions are provided via “central”lines which empty into the great vessels near the heart, such as thecommon vena cava, or directly into the heart, such as via the rightatrium. Infusions are generally provided through vascular access devices(VAD), such as catheters, needles or IV cannulas. There may be placed invessels, such as in the head (e.g. scalp needles), foot (e.g., in thedorsalis pedis vein), the dorsal side-of the hand, the wrist, and theinner aspect of the elbow, known as the antecubital region. An“infiltration” or “extravasation” occurs when radiation is accidentallyinfused into the tissue surrounding the VAD puncture site or the VADoutlet. There may be both significant injury to the tissue as well asloss of medication delivery to the target organ. The hyperosmotic,hypertonic nature of even ordinary IV fluids used in infusions, such assaline and dextrose, may cause localized damage leading to nerve injury,tissue necrosis, and infection, for centrally located catheters,penetration of the VAD outlet into the thorax, particularly into thepericardial sac surrounding the heart may be life threatening.

DISCLOSURE OF THE INVENTION

What is needed is a system and/or method to determine whether medicationis being infused into a tissue region surrounding a VAD puncture site orVAD outlet. Accordingly, the systems and methods described hereinadvantageously feature determining an estimated state of an infusionsite region (ISR), and outputting an alert, alarm and or graphicalnumerical indication of the slate when the estimated state of theinfusion site region and a plurality of actual fluid state parameters ofa fluid delivery channel to the infusion site region indicate aninfiltration. The estimated state of the infusion site region is, incertain embodiments, determined using either a compartment model of theinfusion site region or a continuum model of the infusion site region.

According to certain embodiments of the present disclosure, a medicationdelivery monitoring device is provided. The device includes a userinterface configured to receive input information, and a sensorconfigured to measure a plurality of fluid state parameters of a fluiddelivery channel through which the indication is delivered by a vascularaccess device (VAD) to an infusion site region of the patient. Thedevice also includes a processor configured to determine a state of theinfusion site region based on the plurality of measured fluid stateparameters and the input information, and an output device configured toprovide a communication regarding the state of the infusion site region.

According to certain embodiments of the present disclosure, a method formonitoring medication delivery is provided. The method includesreceiving input information and measuring a plurality of fluid stateparameters of a fluid delivery channel through which the medication isdelivered by a vascular access device (VAD) to an infusion site regionof the patient. The method also includes determining a model state ofthe infusion site region based on the plurality of measured fluid stateparameters and the input information, and providing a communicationregarding the state of the infusion site region.

According to certain embodiments of the present disclosure acomputer-readable medium including computer-readable instructions forcausing a processor to execute a method for monitoring medicationdelivery is provided. The method includes receiving input informationand measuring a plurality of fluid state parameters of a fluid deliverychannel through which the medication is delivered by a vascular accessdevice (VAD) to an infusion site region of the patient. The method alsoincludes determining a model state of the infusion site region based onShe plurality of measured fluid state parameters and the inputinformation, and providing a communication regarding the state of theinfusion site region.

The accompanying drawings, which are included to provide furtherunderstanding and are incorporated in and constitute a part of thisspecification, illustrate disclosed embodiments and together wish thedescription, serve to explain the principles of the disclosedembodiment. In the drawings:

FIG. 1 illustrates a medication delivery monitoring system according tocertain embodiments.

FIG. 2 is a state diagram of the medication delivery monitoring systemof FIG. 1.

FIG. 3A is an exemplary three-compartment model of an infusion siteregion of a patient.

FIG. 3B is an exemplary two-compartment model of an infusion site regionof a patient.

FIG. 3C is a diagram illustrating how Equation 2.9 is derived fromEquation 2.8.

FIG. 3D is a diagram of an infiltration of the two-compartment model ofFIG. 3B.

FIG. 3E is a modeling of an infiltration.

FIG. 3F is an exemplary three-compartment model of an infusion siteregion of a patient.

FIG. 3G is a diagram of an infiltration in the three-compartment modelof FIG. 3F.

FIG. 3H is a set of model equations for modeling an IV infiltration.

FIG. 3I a collection of estimates of parameters for a normal adult foruse with the disclosed compartment model.

FIG. 3J illustrates model prediction of volume in the tissue near thesite of an infusion.

FIG. 3K illustrates a measurement of pressure in the tissue near thesite of an infiltration over tints.

FIG. 3L illustrates a measurement of pressure in immediate IV siteregion tissue compartments of various sizes over time.

FIGS. 4A-4C illustrate three positions of a vascular access device foran exemplary continuum model of an infusion site region of a patient.

FIG. 4D illustrates a solution to the continuum model solution forpressure and displacement.

FIG. 4E illustrates predicted pressure at an infusion site region forthree different injection rates.

FIG. 4F illustrates predicted pressure of an infusion site region for aspecified injection rate.

FIG. 4G illustrates pressure evaluated along s line passing through aninfusion site region.

FIG. 4H illustrates an axisymmetric model of a two-dimensional plane.

FIG. 4I illustrates an asymmetric model snapped from the two-dimensionalplane of FIG. 4H to a three dimensional place.

FIG. 5 is art exemplary process for monitoring the delivery ofmedication using the medication delivery monitoring system of FIG. 1.

FIG. 6 is a block diagram that illustrate an exemplary computing systemthat cm perform certain aspects of the present disclosure in accordancewith one configuration of the present disclosure.

DETAILED DESCRIPTION

There is a problem, in the delivery of fluid medication to an infusionsite region of a patient, of injury resulting front the medication beinginfused into the interstitial tissue space (ITS). Previous attempts atmonitoring the safety of such infusions have been inaccurate orineffective in part owing to their failure to employ informationconcerning the patient, VAD, fluid and history. This and other problemsare addressed and solved, at least in part, by embodiments of thepresent disclosure, which include a medication delivery monitoringdevice. The device includes a user interface configured to receive inputinformation, and a sensor configured to measure a plurality of fluidstate parameters of a fluid delivery channel through which themedication is delivered by a vascular access device (VAD) to an infusionsite region of the patient. The devise also includes a processorconfigured to determine a state of the infusion site region based on theplurality of measured fluid state parameters and the input information,and an output device configured to provide a communication regarding thestate of the infusion site region.

In the following detailed description, numerous specific details are setforth to provide a full understanding of the present disclosure. It willbe obvious, however, to one ordinarily skilled in the art that theembodiments of the present disclosure may be practiced without some ofthese specific details. In other instances, well-known structures andtechniques have not been shown in detail not to obscene the disclosure.

FIG. 1 illustrates a medication delivery monitoring system 100 accordingto certain embodiments, the system 100 includes a user interface 102, anoutlet pressure sensor 104, and a processor 106. The system 100 is used,for example, with an infusion pump 122 (e.g., CareFusion's Alaris Systemmodular infusion pump line) or patient, care unit 124 to monitor theinfusion of a medication 118 from an intravenous (IV) bag through afluid delivery channel 110 and into an infusion site region 114 of apatient 116 via a VAD. Both the infusion pump module 122, and patientcare unit 124 (or “patient control unit” or “PCU” or “controller”),coupled to module 126, can comprise their own user interface, outputs(e.g., displays), and processor (e.g., for receiving pressure signalsand controlling pumping). In certain embodiments, the system 100 (e.g.,to measure resistance to modulate flow. As discussed herein, the terms“infusion site region,” “ISR,” “interstitial tissue space,” “ITS,” “IVsite,” and “IV site tissue” may be used interchangeably. Exemplary VADsinclude catheters, implanted ports, needles, and intravenous cannulas.In certain embodiments, the processor 106 is used to perform selectedinformation processing, while a microcontroller embedded in the infusionpump module 122 is used for lower lever (e.g., fast, real-time)processing such as modulating the flow rate and process the receivedpressure signals to compose the flow resistance.

The user interface 102 is configured to receive input information (or“provided information”) for the system 100, such as patient information,medication information, and/or VAD information, and output informationthrough-as output device 108. The patient information includes theweight of the patient, the height of the patient, the body surface areaof the patient, the age of the patient, and/or the gender of thepatient. In certain embodiments, the patient information includes thepatient's diagnosis and treatment, which may impact factors such as alikelihood tissue at the infusion site region will be edematous. Themedication information includes a chemical nature of the medication, aconcentration of the medication, a rate of infusion dosage (e.g.,ug/kg/min) and flow rate (e.g., mL/h) of the medication, and the natureof at least one diluent or additive associated with the medication. TheVAD information includes a type of the VAD, a dimension of the VAD, thesite in the body of the VAD, a compliance value of the VAD, a resistancevalue of the VAD, and a topology of the infusion network. (e.g., whichchannels are infusing through the same VAD). In certain embodiments, thevalues include measurements, which is a static value that were eitherinput via the user interface 102, stored in the PCU 124, and/or storedon a network connected to the PCU 124, such as on a server wirelessly incommunication with the PCU 124. In certain embodiments, the VADinformation may be available and received from a website (e.g., awebsite for the manufacturer of the VAD) with which the server is incommunication. A wired or wireless input device can be used for the userinterface 102, such as, but not limited to, a keyboard, a touch-screendisplay, a mouse, a microphone, a magnetic card reader, a biometricreader-sensor, a proximity reader, a radio frequency (RF) identificationreader, and a symbology reader. In certain embodiments, acquisition ofthe parameters mentioned above are, at least in part, performed throughan electronic communication of information, such as by using an opticalbarcode or radio frequency identification (RFID) linkage between apatient care unit or infusion put-up and the system 100, to relieve aclinician of the need to enter the information. In certain embodiments,a server connected to the system 100 (e.g., wirelessly or by wire) canacquire this information from extant sources, such as an admission,discharge, and transfer (ADT) system, a clinical laboratory, physicianorder entry (POE), and/or pharmacy.

The outlet pressure sensor 104 is configured to measure a plurality offluid suite parameters of the fluid delivery channel 110. The fluidstate parameters include, for example, the instantaneous and rate ofchange of pressure of the fluid delivery channel, resistance of thefluid delivery channel, capacitance of the fluid delivery channel, andfluidic impedance of the fluid delivery channel. In certain embodiments,the pressure is measured at an outlet of the fluid delivery channel 110,such as at the infusion site region 114 where the medication 118 leavesthe fluid delivery channel 119.

In certain embodiments, the fluidic input resistance to the infusiontubing network 110 is measured based on small scale modulations,introduced by the processor 106, in the average infusion rate of themedication 118. In certain embodiments, two basic approaches areemployed to measure the fluidic intake resistance. One approach is usedfor rates above 50 mL/h. The remaining, more complex approach is usedferrates at or below 50 mL/h. The higher rate approach, in principle,dynamically adjusts the flow rate typically in a square wave patternaround the mean programmed value and measures the pressure response tothese modulations. The find pressure at the high rate is subtracted fromthe final pressure at the low rate and this difference divided by thedifference in the flow rates. The result is a ‘dynamic’ input-resistanceof the field path. The resulting resistance is filtered using median andaveraging methods to eliminate noise due to ambulation, etc. The lowerflow method achieves a similar result however, the modulation and thesubsequent processing of the pressure signals is somewhat more complexin order to avoid undue variation in the flow pattern that could beundesirable for some medications. Additional information regardingapproaches to measure fluidic input resistance can be found in U.S. Pat.Nos. 5,803,917 and 6,416,291, which are incorporated by reference hereinin their entirety. The small scale modulations are associated withresulting pressure variations in the fluid deli very channel 110 tofurther measure the capacitance and the impedance at an input to thefluid delivery channel 110. In certain embodiments including those wherefluid impedance is measured, the outlet pressure sensor 104 isconfigured to be of high resolution and of high accuracy.

The processor 106 is configured to determine a state of the infusionsite region 114 based on the plurality of measured fluid stateparameters and the input information. In certain embodiments, theprocessor 106 is configured to record at least one of instantaneousfluid state parameters, filtered fluid state parameters, and long termtrends of fluid state parameters. Use processor 106 is furtherconfigured to model the state of fluids and proteins (e.g., proteinmass, tissue porosity) at the infusion site region 114 based on thepressure of the fluid delivery channel, resistance of the fluid deliverychannel, and the input information (e.g., the patient information,medication information, and/or VAD information). In certain embodiments,the model is farther based on the impedance of the fluid deliverychannel. As discussed herein, in certain embodiments, the term“impedance” incorporates the three orthogonal parameters of resistance,compliance and inertance. In certain embodiments, the model employs pumpflow of the fluid delivery channel 118. In certain embodiments, themodel is further employs the history of the measured fluid stateparameters, such as the history of the infused medication 118 (e.g.,volume of the infused medication over time). The history of the measuredfluid state parameters (e.g., volume of the infused medication overtime) is configured to be stored in a memory 120.

In certain embodiments, the model is either a discrete compartmentmodel, a continuum model, or combination of both. The compartment modeldescribes quantity and pressures of fluids and proteins (i.e., the majorsolute of blood plasma fluid) and from these derives the expectedvolumes, deformations and pressures in the tissue surrounding theinfusion site region 114. The continuum model describes similarparameters but computes them employing a much higher resolution physicalmodel, of the elasticity and porosity of the ITS. The compartment modelconceptualizes and segregates the body and its fluids into a smallnumber of homogeneous regions, while the continuum or finite-elementmodel describes the properties of the body and its fluids in threephysical dimensions over time. In certain embodiments, the continuummodel is employed in the course of refining the structure and parametersof the compartment model, and, with the appropriate processing power, isimplemented directly in a real-time system.

The approaches complement each other since the compartment modelsimulates flow between distinct regions and the continuum modelsimulates flow within a region. Further detail regarding these models,as well as how they are generated, is described in further detail belowBased on a comparison of the model estimate of unfiltrated andinfiltrated states, the output device 108 is configured to provide acommunication regarding the state of the infusion site region 114, suchas to indicate that the infusion site region 114 has been infiltrated.For example, the model is configured to predict that no IV fluid ispresent in the ITS, which is the ‘normal’ state, and configured topredict any positive value of IVD as a progressively deterioratingcondition.

Based on knowledge of IV flow, measured pressure and resistance andparameters such as compliance and porosity which correlate withoperator-entered patient parameters such as age and IV VAD location, themodel predicts the state of the interstitial tissue including amounts offluid added, to the interstitial space, amount of protein transportedand expected pressure values. If the fluid state parameters measured bythe sensor 104 are not within a pre-determined range of thecorresponding expected fluid state parameters, then the processor 106sends a communications to the output device 108. In certain embodiments,the output communication is an alert, alarm and/or graphical/numericalindication of the state. The output communication is, in certainembodiments, a threshold driven event. In certain embodiments, theoutput communication presents the state of the interstitial tissue as acontinuous variable with and without generation of an alarm/alert event.In certain embodiments, a communication can be sent based on otherproperties associated with the patient, such as, but not limited to, (1)the fluid volume, pressure, compliance, and resistance infusion pathway,(2) the fluid volume, pressure, protein mass, compliance, and porosityof an interstitial tissue matrix, (3) and the fluid volume, pressure,protein mass, compliance, and resistance of a peripheral vessel. Therates of change of these values may, in certain embodiments, be anindependent parameter of state. For example, determining the complianceof an infiltrated tissue site region surrounding the vessel site might,in certain embodiments, be determined by trending the rate of change ofpressure against volume pumped. As compared to a vessel, wherecompliance is generally high, and pressure generally does not changeover a given volume of fluid infused, in the infiltrated tissue site,pressure can increase over time, depending on pump flow rate and itsrelation to lymphatic uptake, during at least past of the course of theinfiltration. For example, at 20 mL/h, it is expected that lymphaticuptake would be overwhelmed in a 10 kg child, thus if the vessel wall isbreached by the cannula, pressure would be expected to increase for aperiod of time. The disclosed compartment model predicts that aspressure rises, fluid begins to diffuse away more quickly so thatultimately a relatively steady state pressure is attained.

Once the output device 108, which is illustrated in FIG. 1 as a display,receives the communication, the output device 108 is configured todisplay the communication, such as in the form of a value, an alert, oran alarm. The communication can be, for example, a visible communication(e.g., an onscreen message or a graphical indicator such as a bar graphor trend plot), an audible communication (e.g., a beeping alarm), adifferent type of sensory communication (e.g., a vibration), or anycombination thereof. In certain embodiments, the output device 108 isconfigured to display both current and expected fluid state parametersthroughout the time the medication 118 is infused into the patient 116,regardless of whether the expected fluid state parameters indicate aninfiltration. Such display is advantageous in that it provides anoperator with a continuing status of the infusion site region 114 of thepatient 116. In certain embodiments, the output device 108 is configuredto display a deviation of the current fluid state parameters fromexpected fluid state parameters. For example, if the expected IV fluidin an ITS is zero, the output device 108 will display the model estimateof the IV fluid that is present in the ITS. In certain embodiments, thecommunication includes an estimate, by the disclosed model, of a keystate variable, e.g., the estimated intravenous fluid in the infusionsite region 114, which should, under normal conditions, be zero. Incertain embodiments, as disclosed above, the estimated key statevariable is presented, by the output device, such as to allow aclinician to allow the clinician to decide if any action is appropriate.In certain embodiments, the estimated key state variable is used as analarm threshold by the output device In certain embodiments, thethreshold can depend on the size of the patient's infusion site region114 (e.g. an infusion site region 114 for an adult, child, or neonate),the likely toxicity of the medication, e.g., for a highly vesicantinfusion, the threshold should be lower than a saline solution infusionfor hydration.

The output device 108 is illustrated as a display. Other types of outputdevices 108 can be used, including, without limitation, a printer,audible indicators such as speakers, or other visual indicators such asdisplay screens, including a cathode ray tube (CRT) display, vacuumfluorescent display (VFD), light emitting diode (LED) display, plasmadisplay panel (PDF), liquid crystal display (LCD), organic lightemitting diode (OLED), or surface-conduction electron-emitter display(SED). Similarly, the communication provided to the output device 108can be, for example, a visible communication (e.g., an onscreenmessage), an audible communication (e.g., a beeping alarm), a differenttype of sensory communication (e.g., a vibration), or any combinationthereof. The output device 108 is configured so display of otherwiseoutput information provided by the processor 106, such as communicationsidentifying whether the measured fluid state parameters are within apre-defined range of the expected fluid state parameters.

FIG. 2 is a signal flow and processing high level slate diagram 200 ofthe medication delivery monitoring system of FIG. 1. The model 210,generated by processor 106, is based on various inputs, including, forexample, patient information 212 (e.g., weight and other non-varyingattributes), fluid delivery channel pump, flow 222 of the medication 118over time, fluid delivery channel (e.g., IV line) pressure 218 over tune(e.g., with reference to the history of recorded values of measuredfluid delivery channel pressure, which is stored in memory 120), fluiddelivery channel resistance 220 over time, and VAD information 216. Incertain embodiments, the model 210 is also based on an input thatincludes medication information 214. The fluid delivery channel pumpflow 222 of the medication 118 over time, fluid delivery channelpressure 218 over time, fluid delivery channel resistance 220 over time,and VAD information 216 is also provided for signal processing 228, suchas by processor 106. The output of the model 210, including estimatedstate values 224 of the infusion site region 114 of the patient 116(e.g., how much infused fluid has infiltrated the infusion site region114, or protein, a critical factor in fluid transport between thevasculature, lymph and ITS, is in the infusion site region 114), isprovided to decision logic 230 (e.g., in processor 106) for processingwith, for example, a currently measured fluid delivery channel pressure238, a currently measured fluid delivery channel resistance 240, and acurrently measured pressure versus volume infused 232. These currentlymeasured values 238, 240, and 232 are provided by the signal processing228, and are further provided for presentation processing 250, includingpossible sealing and offset smoothing range dynamics, to optionally bedisplayed on an information display 252, such as the output device 108.For example, the expected pressure and resistance 234 of the fluiddelivery channel 110 and the currently measured fluid delivery channelpressure 238 and resistance 240 can be displayed to an operator formonitoring the infusion of the medication 118 to the patient 116.Returning to the decision logic 230, if the currently measured values238, 240, and 232 and the model estimate values 224 indicate that theinfusion site region 114 has been infiltrated, as based on providedstate alarm and alert thresholds 216, which may be functions of thepatient information 212 and the-medication information 224, then analarm and/or alert 234 is indicated, by, for example, the output device108, or, in certain embodiments, a control 234 of the medicationinfusion to the patient 116 is adjusted, such as by the pump associatedwith the medication delivery monitoring device 100.

FIG. 3A is an exemplary compartment model 300 of an infusion site region114 of a patient 116. As shown in FIG. 3A, a generalized and highlysimplified example, a compartment model divides the body's fluid intodiscrete homogeneous compartments: plasma (within the blood vessel) 302,IV site immediate tissue 304 (in which IV fluid may be misdirected), andail other body tissue 306 (i.e., all regions outside the immediate fieldof the IV site). The model calculates the fluid volume and protein mass(a primary influence on fluid transport between compartments) withineach of these compartments 302, 304, and 300 over the course of asimulated infiltration based on controlled flow from the pump andmeasured pressures as well as properties of the tissue estimated fromuser inputs describing the site and patient age/weight. An increase influid volume (e.g., the sum of blood plasma and IV fluid) within theinterstitial space is a primary indicator of a growing complicationlikely due to misplacement of the vascular access device.

The expressions for fluid and protein transport are described by sixordinary differential equations, as described in further detail below.Pressure in the immediate IV site region tissue compartment iscalculated from a pressure-volume (compliance) curve derived frompatient weight and site description, because the weight and site isknown. This type of model describes the transport of fluid and proteinbetween each compartment using ordinary differential equations (ODEs).This transport of fluid and protein is a result of the microvascularexchange system. A more sophisticated model includes lymph drainage andan exogenous, time-dependent fluid input 308 as would occur during aninfiltration or deliberate subcutaneous injection. This moresophisticated model allows the average pressure and total volume offluid in each compartment to be calculated. Because each compartment isassumed to be homogeneous this model does not show fluid movementinternal to the compartment. However, compartment models described byODEs are simpler than continuum models, and therefore are easier todefine and faster to solve. Compartment models have been used with greatsuccess in the held of pharmacokinetics.

To explain in more detail how the compartment model was developed forthis application, two exemplary, simplified embodiments of a compartmentmodel will now be described in greater detail. Compartment models (orlumped element models) predict quantities and rates of change (e.g.,transport) of a substance in different compartments. First, a twocompartment model FIG. 3B, which considers the circulatory system(plasma) and the rest of the tissue (interstitial tissue space) isdescribed. Then the model is extended to a three-compartment system,incorporating a local compartment that describes fluid near the infusionsite.

A simplified, two-compartment model is first considered that divides thebody's fluid into two homogeneous compartments, the plasma (PL) andinterstitial (body) tissue (B), as seen in FIG. 3B. This model estimatesthe volume of fluid, V, and protein mass, M, in both compartments. Thefluid volume of the plasma and body tissue is denoted as V_(PL) andV_(B), and the protein mass in each compartment as M_(PL) and M_(B). Ina more complete model to be described following this model, a source ofexogenous fluid and protein will be added to the plasma compartmentsimulating a normally placed VAD, or to the interstitial tissuesimulating an infiltrated condition.

In the simplified model shown in FIG. 3B, the transport of fluid, i.e.the time rate of change of its volume, dV_(b)/dr, and protein,dM_(B)/dr, into the interstitial tissue is defined as the differencebetween transport across the capillary membrane into the tissue, J_(C)and Q_(C), and the lymph transport out of the tissue into the plasma,J_(L) and Q_(L), as well as fluid loss via perspiration from thecirculatory system, J_(per):

dV _(B) /dt=J _(C) −J _(L) −J _(per,)  (2.1)

and

dM _(B) /dt=Q _(C) −Q _(L,)  (2.1)

Net transport (i.e. time rate of change of fluid and protein) into theplasma are given by the difference between lymph flow J_(L) andcapillary flow J_(C), with additional fluid input from ingestion,J_(in), and infusion, J_(iv), and loss due to urination, J_(ur):

dV _(PL) /dt=J _(L) −J _(C) +J _(in) +J _(iv) −J _(ur)  (2.3)

and

dM _(PL) /dt=dM _(B) /dt=Q _(L) −Q _(C)  (2.4)

Fluid exchange occurs across the capillary membranes (from vessel (PL)to interstitial tissue (B) is modeled according to Starling's Law ofmembrane filtration.

J _(C)=κ[(P _(PL) −P _(S))−σ(Π_(PL)−Π_(B))]  (2.5)

In Starling's Law, fluid flow is driven by two mechanisms. First,Darcy's Law states that flow through a porous medium (here, thecapillary membrane that separates the arterial and venous blood vesselsfrom the surrounding interstitial tissue) is proportional to thedifference in fluid hydrostatic pressure (ΔP=P_(PL)−P_(B)). Second,fluid flow follows an osmotic gradient (ΔΠ=Π_(PL)Π) caused bydifferences in protein concentration across the capillary membrane asdescribed by Equations 2.6 and 2.7.

Proteins are considered because they are the most important solutesaffecting fluid transport between the circulation and body tissue. Thisis due to protein's low diffusivity compared to smaller solutes, such asions. Any difference in protein concentration between Compartmentscauses a colloid osmotic pressure gradient, ΔΠ, that affects fluid flowacross the capillary membrane according to Starling's Law (see Equation2.5). The relationship between protein concentration, C, and colloidosmotic pressure, Π, in each compartment is given as

C _(PL)=1.522·Π_(PL)  (2.6)

C _(B)=1.522·Π_(B)  (2.7)

The value 1.522 is derived from a linear regression fit topressure-concentration data. The osmotic effects of small solutes areignored because their effect on fluid flow is generally lesssignificant.

The magnitude of transport (e.g., flow) due to the osmotic gradientdepends upon the reflection coefficient (σ) of the solute, which is ameasure of the solute's diffusivity. Solutes that readily diffuse acrossthe membrane have less impact on fluid flow (smaller σ values,approaching 0), while solutes that can barely diffuse have more impacton fluid flow across the capillary membranes (larger σ values,approaching 1). According to one embodiment, in the disclosed model,protein has a high σ value (0.96-0.99), while ions would have much lowera values (on the order of 0.05). For this reason the osmotic effects ofions are not included. The capillary fluid filtration coefficient (κ) isair experimentally determined constant which affects the transport rateof both proteins and fluid. The value κ=121.1 mL/mmHg·hr is used.

Protein transport across a membrane is described by both convection anddiffusion according to the following formula:

$\begin{matrix}{Q_{c} = {{{- p}\frac{C}{x}} + {{C_{PL}\left( {1 - \sigma} \right)}J_{c}}}} & (2.8)\end{matrix}$

Protein diffuses proportionally (according to the membrane permeability,at constant volume) to the concentration gradient

$\left( \frac{C}{x} \right).$

Protein is carried across the membrane via convection proportionally toboth capillary fluid flow (J_(C)) and the concentration of protein inthe plasma (C_(PL)). Reflection coefficient σ, described above, is ameasure of the protein's diffusivity and small values correspond toreadily diffusive solutes. Thus, (1−σ) will be near 1 (or readilydiffusive solutes (ions) and near 0 for less diffusive solutes(proteins). The capillary permeability surface area product, μ, is equalto P_(m)/δ, and is a measure of the membrane permeability per unit area.The surface area product, μ, can be thought of as the amount of plasmavolume that gives up its solute contents to the interstitial fluid perunit time (on the order of 73 mL/hr). Equation 2.8 is a first orderlinear differential equation for C(x) where C(0)=C_(PL) and C(δ)=C_(g).Integrating along the x-axis (across the membrane from x=0 to x=δ, seeFIG. 3C) using the integrating factor

$^{\frac{{- {x{({1 - \sigma})}}}J_{C}}{\mu}}$

leads to the following expression for protein transport acrosscapillaries (Q_(C)):

$\begin{matrix}{Q_{C} = {\left( {1 - \sigma} \right){J_{C}\left\lbrack \frac{{CPL} - {{CB} \cdot ^{\frac{{- {({1 - \sigma})}}J_{C}}{\mu}}}}{1 - ^{\frac{{- {({1 - \sigma})}}J_{C}}{\mu}}} \right\rbrack}}} & (2.9)\end{matrix}$

Fluid is transported through the lymph from the interstitial tissue backto the plasma,

J _(L) =J _(LB)+λ(P _(B) −P _(B0))  (2.10)

Lymph fluid flow is described in Equation 2.10 as a basal lymph flowrate (J_(L0)) plus a term proportional to the deviation from normalinterstitial fluid pressure (P_(B)−P_(B0)). The proportionality constantis the lymph sensitivity (λ) to changes in pressure, which is on theorder of 43.1 mL/mmHg·hr.

Protein is removed from the interstitium and travels back to the plasmavia the lymph flow, which is assumed to be convective and proportionalto the interstitial protein concentration (C_(B)),

Q _(L) =J _(L) ·C _(B)  (2.11)

No protein is assumed to be lost from the system. However, the modelincludes several sources of fluid loss: insensible water loss (whichoccurs through membranes, primarily the lungs), perspiration, andurination. Insensible loss is modeled as constant fluid outflow becausewater leaves from the wet mucous membranes of the lung as a necessaryconsequence of breathing. The expected impact of systemic water lossfrom the entire circulatory system on the regional modeling ofinfiltration is small, yet this term is employed for completeness.

To model an IV infiltration, the IV input (“infusion”) is “moved” fromthe vein (FIG. 3B) to the interstitial tissue compartment (FIG. 3D).FIG. 3D models an IV needle puncturing the vein and infusing fluid intothe surrounding interstitial tissue.

Fluid is not cleared from the body tissue by the lymph vessels andperspiration (J_(L), and Jper) as quickly as fluid enters from theplasma by the capillaries (J_(C)) from the infiltrated IV needle(J_(in)), fluid builds up in the interstitium when the IV fluid input ismoved from the vein to the interstitium (FIG. 3E). An example simulationis shown in FIG. 3E, where fluid is infused at a rate of 100 mL/hr intothe bloodstream for the first 5 hours. At time t=5 hours the fluid inputis moved to the body tissue compartment simulating an infiltration. Bytime t=7 hours the body interstitial fluid volume reaches a new steadystate volume, 24 mL above the original steady state volume during normalinfusion into the bloodstream.

The above simplified, two-compartment model treats all of theinterstitial tissue in the entire body as one compartment. However,fluid volume changes in the vicinity of the injection site are describedmore accurately by using a local interstitial compartment separate fromthe rest of the body. Fluid movement away from am infiltrated site canoccur principally by diffusion through the interstitial tissue matrixand by flow through the lymph vessels.

To provide a better approximation of the actual anatomy, the originalinterstitial tissue compartment is replaced by two compartments: an arm(A) interstitial tissue and a body (B) compartment in FIG. 3F. fluidenters the system by infusion into a third compartment the blood vesselcontaining plasma. Fluid leaves the system by both urination from theplasma and perspiration from the interstitium through the skin. Plasmaexchanges its fluid component with the tissue compartments throughcapillary and lymph vessels. With a model of this complexity, fluidmovement between tissue compartments is considered insignificantrelative to vessel-tissue movement. The fluid volume of the armtissue/immediate IV site region tissue compartment is denoted as V_(A)and the protein mass of the arm interstitium compartment as M_(A). Usefluid volume and protein mass of the body tissue compartment becomeV_(B) and M_(B). A local/arm vessel/plasma compartment is unnecessarybecause the plasma fluid flow rate between vessels in the arm and plasmaelsewhere in the body is so much faster than fluid flow between plasmaand tissue that it can be approximated as instantaneous.

To extend the two-compartment model to the three-compartment model, thesame basic equations are used and modified to reflect the differentsizes of the two tissue compartments. A new parameter, prop, is definedto be the proportion of the arm interstitial volume in the region of anIV site to be modeled compared to the total interstitial volume.Initially, prop=1.5/70, as the average weight of an adult human forearmis around 1.5 kg and the subject considered weighs 70 kg.

The prop parameter can be thought of as the proportion of capillary andlymph vessels servicing the local/arm compartment. Since the arm is 1/40of the body, then using simple proportioning, approximately 1/40 of thebody's capillary and lymph vessels may be available to move fluidbetween the plasma and the arm interstitial tissue compartment. Theother 68.5/70 of the capillary and lymph vessels move fluid between theplasma and the body interstitium compartment. Consequently, the fluidtransport for a given pressure difference will be scaled to thecompartment size.

The capillary permeability surface area product, μ, is scaled by propfor the arm interstitium compartment and (1−prop) for the bodyinterstitium compartment (recall that μ is permeability divided bymembrane thickness (μ=p/δ)). Intuitively this makes sense because thenumber and surface area of in each tissue compartment is scaled down.

In the three-compartment model, the transport of fluid and proteindepends on two separate lymph and capillary flow rates for eachinterstitial tissue compartment. Equation (2.5) that describes fluidtransport across capillaries is scaled by prop to become the equationfor fluid flow across the capillaries to the arm compartment:

J _(CA)=prop·κ[P _(PL) −P _(A))−σ(Π_(PL)−Π_(A))]  (2.12)

and fluid transport across the capillaries to the body compartmentbecomes:

J _(CA)=(1−prop)κ[(P _(PL) −P _(B))−σ(Π_(PL)−Π_(B))]  (2.13)

The equation for fluid transport from the interstitium to the plasmathrough the lymph (Equation 2.10) is similarly sealed by prop for thearm compartment:

J _(LA)=prop(J _(L0)+λ(P _(A) −P _(A0)))  (2.14)

and (1−prop) for the body compartment:

J _(LB)=(1−prop)(J _(L0)+λ(P _(B) −P _(B0)))  (2.15)

Under non-infiltrated conditions, both arm and body interstitialcompartments are assumed to have the same normal hydrostatic pressure(i.e., P_(B0)=P_(A0)) when the patient is supine.

The equations for both capillary and lymph protein transport do not needto be explicitly sealed by prop because they contain the expressions forfluid flow (J_(CA)and J_(CB)), which have already been sealed. Thus, themodified capillary protein transport equations are (compare withEquation 2.9, note the subscripts denote source-destination of themovement e.g. “CA” means capillary to arm [interstitial tissue] anddenotes capillary to body):

$\begin{matrix}{{Q_{CA} = {\left( {1 - \sigma} \right){J_{CA}\left\lbrack \frac{C_{PL} - {C_{A} \cdot ^{\frac{{- {({1 - \sigma})}}J_{C}}{\mu \cdot {prop}}}}}{1 - ^{\frac{{- {({1 - \sigma})}}J_{C}}{\mu \cdot {prop}}}} \right\rbrack}}}{and}} & (2.16) \\{Q_{CB} = {\left( {1 - \sigma} \right){J_{CB}\left\lbrack \frac{C_{PL} - {C_{B} \cdot ^{\frac{{- {({1 - \sigma})}}J_{C}}{\mu \cdot {prop}}}}}{1 - ^{\frac{{- {({1 - \sigma})}}J_{C}}{\mu \cdot {prop}}}} \right\rbrack}}} & (2.17)\end{matrix}$

The lymph protein transport equations are now (compare with Equation2.11):

Q _(LA) =J _(LA) ·C _(A)  (2.18)

and

Q _(LB) =J _(LB) ·C _(B)  (2.19)

To model an IV infiltration, the IV input (J_(iv)) is moved from theplasma to the immediate IV site region/arm tissue compartment (FIG. 3G).For the adult case, to replace body fluids, thereby holding localperipheral venous pressure relatively constant, the sum of inward flows(J_(in)+J_(iv)) is assumed constant at 100 mL/hr, and balanced by theurination term resulting in typical peripheral venous pressures of 0 to10 mmHg in a supine position. This models an IV needle accidentallypuncturing the vein, infusing fluid into the surrounding interstitialtissue, but not into interstitial tissue far away from the injectionsite.

FIG. 3H summarizes the complete set of model equations. Estimates ofparameters for a normal, reclining 70 kg adult can be found in FIG. 3I.In FIG. 3I, interstitium parameters (indexed by I) apply to both thebody interstitium and arm interstitium compartments, with the bodyinterstitium versions being scaled by (1−prop) and the arm interstitiumversions scaled by prop.

Behavior of infiltrations in the arm (antecubital site) in adults fortypical infusion rates up to 100 mL/hr is now considered. With infusionrates below 15 mL/hr, the volume of fluid in the interstitial tissuesurrounding the cannulation site is estimated to increase by less than10 percent during infiltration. FIG. 3J illustrates model prediction ofvolume in the tissue near the site of an infusion. Fluid is showninfused at various rates into the plasma until time t=5 hours. Next, theVAD “infiltrates” the tissue, resulting in the local infusion siteregion volume increasing toward a steady state level The steady state isachieved since the accompanying increased pressure forces fluid outthrough the lymph and the surrounding tissue until equilibrium isreached. At time t=34 hours, the infiltration is removed and theinfusion into the plasma resumes, the excess fluid in the infusion siteregion diminishes toward normal at a rate somewhat proportional to thepeak volume.

At most rates, pressure increases nonlinearly because of therelationship between the infusion site region's volume and pressure. Thenormal arm tissue hydrostatic pressure is −0.7 mmHg in the supine adult.The three compartment model estimates pressure in the arm tissue inranges front about −0.4 mmHg with an infusion of 5 mL/hr to about 17mmHg with an infusion of 100 mL/hr. At 40 mL/hr, the pressure increasesto 3.2 mmHg within 30 hours of infiltration (FIG. 3K). FIG. 3Killustrates pressure in the interstitial tissue near the sites of aninfiltration. Fluid is being infused at 40 mL/hr into the vein untiltime t=5 hours. Then, the needle infiltrates the tissue and theinterstitial tissue pressure increases. The increase is nonlinearbecause the tissue compliance is nonlinear (the tissue can stretch to amaximum after which a small increase in volume greatly increasespressure). At time t=34 hours, the infiltration is removed and the 40mL/hr infusion into the vein resumes. Like volume, pressure dissipatesmore rapidly than it built up. These volumes and pressures are averagesfor the compartments. FIG. 3K uses 1.5/70 as the proportion and showedpressure response to infiltration at various infusion rates.

FIG. 3L illustrates the model prediction of the pressure response toinfiltration at 100 mL/hr as plotted in arm compartments of differentsizes. Intravenous fluid is being infused at 100 mL/hr into the veinuntil time t=5 hours. Then, the VAD infiltrates the tissue resulting inthe interstitial tissue pressure increasing. Smaller compartments showgreater maximum pressure, revealing pressure changes close to theinjection site. At time t=34 hours, the in the pump flow is returned tothe vein. With an antecubital arm compartment of 0.5 kg (for a 70 kgadult), the pressure during infiltration is greater than 70 mmHg. Oneprevious study found that the average pressure at the injection siteduring 100 mL/hr infiltration ranges from about 0.5 mmHg to about 2 mmHgfor each mL/h.

Having detailed the compartment model, FIGS. 4A-4C illustrate threepositions of a vascular access device for an exemplary continuum model400 of an infusion site region 114 of a patient. Specifically, FIG. 4Aillustrates an etiology of infiltration/extravasation of a cannula 402in a vein, FIG. 4B illustrates an etiology of infiltration/extravasationof a positional cannula 402, and FIG. 4A illustrates an etiology ofinfiltration/extravasation of a cannula 402 that has penetrated intointerstitium tissue, resulting in an infiltration. If, in FIG. 4C, thefluid delivered by the cannula were toxic, the condition would bedefined as an extravasation. The continuum model can be used tocorroborate the predictive ability of the discrete compartment model,and to obtain insight into the behavior of the infiltrated infused fluidwith the media of the interstitial space. Current real-time batteryoperated processors are not yet able to provide this level ofcomputation for direct application, however the growing use of wirelessconnected servers might make performing such computations for a largenumber of pumps in near real time feasible in the future.

A continuum model 400 describes an infiltration by considering theinjected fluid's motion from the injection site and its interactionswith a region of surrounding tissue. Two coupled partial differentialequations model a poroelastic tissue using Darcy's Law and a soliddeformation equation, as described in further detail below. In certainembodiments, an ideal continuum model is a more appropriate type ofmodel in that it could exactly describe the motion of the injectedmedication in three dimensions. In certain embodiments, a continuummodel must realistically include simplifications due to a limitedknowledge of the tissue properties, initial conditions, and boundaryconditions. In addition, continuum models are represented mathematicallyby partial differential equations, which are usually not solvable inclosed-form; instead, a computer-based numerical solver is used to findsolutions. A simplified model of fluid flow in tissue is described byDarcy's Law of flow through porous media in which the local flow rate isproportional to the pressure gradient. Fluid flow in biological tissueis often modeled using theories of porous media flow in which a fluid isrestricted to move through small pores in a solid medium. Poroelasticmodels are more complicated models in which the porous medium haselastic properties. The porosity depends not just on the position in amaterial, but also on the properties of the fluid flow. One motivationfor a poroelastic model is that the properties of the interstitialtissue can change dramatically depending on the presence or absence ofadded fluid: one study reports that the hydraulic conductivity canchange by a factor of 250,000 during an infiltration. The continuummodel is based on the theory of poroelasticity and is described by twocoupled partial differential equations (PDEs).

A continuum model, as opposed to a compartment model, describes themotion of an injected fluid and its interactions with a region ofsurrounding tissue. The continuum model provides information (such aspressure or velocity) at every point in the region and at every instanceof time. Mathematically, a continuum model is described using a systemof PDEs.

The Navier-Stokes equations a common continuum model which describe flowof a single fluid, for example, water flowing through a metal pipe. Inthe case of fluid flow in biological tissue, the Navier-Stokes model isinsufficient because it fails to account for the solid structure(collagen and elastin) present throughout the tissue. A more appropriatemodel is based on the empirically-derived Darcy's Law, which describeslow-speed fluid through a porous medium, such as groundwater throughsoil. Darcy's Law alone does not model the compliance or elasticity ofthe tissue, so it cannot predict phenomena such as swelling from edema.In order to account for deformation of the tissue, Darcy's law isapplied in combination with an elastic deformation model. Thecombination, called poroelasticity, describes a solid elastic matrixthrough which a pure fluid may flow. The fluid flow and deformationmodels are coupled so flow induces deformations, while deformations inturn affect the fluid flow. Poroelasticity is commonly used as a modelfor fluid flow through biological tissue. In certain embodiments, analternative model called mixture theory can be used to describe fluidflow in biological tissue.

In certain embodiments, the poroelastic model is implemented in COMSOLMultiphysics, a software package designed to numerically solvecontinuous physical problems. Poroelasticity is included as a predefined“Multiphysics” mode in COMSOL, although some modifications can improvethe relevance of the model to the problem. The following sectionsdescribe the governing equations, parameters and boundary conditionsused to model both the fluid flow and elastic deformation, as well asthe results from the disclosed model.

The poroelastic model is described by two coupled partial differentialequations. The first equation governs the fluid flow through the tissueand is based on Darcy's Law. Darcy's law is an empirically derivedstatement that relates fluid flow to the pressure gradient. It assumes alow flow rate and can also be derived from the Navier-Stokes Equationsusing several; simplifying assumptions. Darcy's law states

$\begin{matrix}{q = {{- \frac{K}{\rho_{j}g}}{\nabla p}}} & (3.1)\end{matrix}$

where q is the discharge of fluid per unit area (flux), K is thehydraulic conductivity, ρ_(f) is the fluid density, g is thegravitational acceleration, and p is the fluid pressure.

Equation (3.1) is used in conjunction with a continuity equation toderive the fluid flow governing equation in the poroelastic model. Thecontinuity equation states that the rate at which fluid mass enters aregion is equal to the rate at which mass leaves a region. This can beexpressed as

$\begin{matrix}{{\frac{\partial\left( {\rho_{f}\theta_{s}} \right)}{\partial t} + {{\nabla{\cdot \rho_{f}}}q}} = {\rho_{f}Q_{source}}} & (3.2)\end{matrix}$

where θ_(x) is the fraction of the volume available for fluid flow andQ_(source) is the strength of a fluid source or sink (l/s) within theregion itself. Substituting in the equation for flux from Eq. (3.1) intoEq. (3.2) yields

${\frac{\partial\left( {\rho_{f}\theta_{s}} \right)}{\partial t} + {\nabla{\cdot \left\lbrack {\rho_{f}\left( {\frac{- K}{\rho_{f}g}{\nabla\rho}} \right)} \right\rbrack}}} = {\rho_{f}Q_{source}}$

For an incompressible fluid ρ_(f) is constant and can move outside thedivergence operator. Dividing: through by ρ_(f) gives us

${\frac{\partial\theta_{s}}{\partial t} + {\nabla{\cdot \left( {\frac{- K}{\rho_{f}g}\nabla} \right)}}} = Q_{source}$

In the disclosed model, the ability of the solid structure to expand andcontract is analogous to pressure sources or sinks. If the solidexpands, the pressure in the region will decrease assuming no additionalfluid enters the region. Similarly, if the solid contracts, the pressureincreases, acting as a pressure source. This is expressed by letting

$Q_{source} = {{- \alpha_{b}}\frac{\partial e}{\partial t}}$

where ∂e/∂t is the time rate of change of volumetric dilation (s⁻) fromthe equation for the elastic deformation and α_(B) is an empiricalconstant called the Biot-Willis coefficient. The resulting governingequation is

$\begin{matrix}{{\frac{\partial\theta_{s}}{\partial t} + {\nabla{\cdot \left( {\frac{- K}{\rho_{f}g}{\nabla p}} \right)}}} = {{- \alpha_{b}}{\frac{\partial e}{\partial t}.}}} & (3.3)\end{matrix}$

The equation can be simplified by using the chain rule to define

$S_{\alpha} = {\rho_{f}{g\left( \frac{\partial\theta_{s}}{\partial p} \right)}\left( \frac{\partial p}{\partial t} \right)}$

as the storage coefficient (m⁻¹). The storage coefficient is typicallyfound experimentally, and it can be defined either in units of m⁻¹, usedhere, or Pa⁻¹. The difference between the two definitions is a factor ofρ_(f)g. The equation implemented in the continuum model is

${{\left( \frac{S_{\alpha}}{\rho_{f}g} \right)\frac{\partial p}{\partial t}} + {\nabla{\cdot \left( {\frac{- K}{\rho_{f}g}{\nabla p}} \right)}}} = {{- \alpha_{b}}{\frac{\partial e}{\partial t}.}}$

In the disclosed model the empirically derived value α_(B)=1 is used forthe Biot-Willis coefficients The value for hydraulic conductivity is setso K=10⁻⁷ m/s, which is atypical value found experimentally for thesubcutaneous tissue of rats. The storage coefficient, Ss, is set to 10⁻⁸m⁻¹. The fluid is assumed to be mostly water, therefore the density isρ_(f)=1000 kg/m³.

Following the derivation, the stress tensor z for the tissue is

τ=2 Gε+λeI−pI

where ε is the strain tensor, e is the volume dilation of the tissue, pis the local fluid pressure, λ is a Lamé constant which characterizesthe material along with the shear modulus G. Here, it is assumed thatthe tissue is a linear and isotropic elastic material. In terms of thedisplacement vector u, the strain tensor is written as

$ɛ = {\frac{1}{2}\left( {{\nabla u} + \left( {\nabla u} \right)^{T}} \right)}$

and the volume dilation as

e=∇·u

Neglecting momentum and any external forces, the equation of motion is

∇·τ=0

Substituting the values of z, s and e gives

G∇2u+(G+λ)∇(∇·u)−∇p=0

The elastic parameters (G, A) can be converted to the modulus ofelasticity E and Poisson's ratio v:

$G = \frac{E}{2\left( {1 + v} \right)^{\prime}}$$\lambda = \frac{Ev}{\left( {1 + v} \right)\left( {1 - {2v}} \right)^{\prime}}$

leading to the elastic equation used by COMSOL:

${{\frac{E}{2\left( {1 + v} \right)}{\nabla^{2}u}} + {\frac{E}{2\left( {1 + v} \right)\left( {1 - {2v}} \right)}{\nabla\left( {\nabla{\cdot u}} \right)}}} = {\nabla p}$

In the implementation of the elastic model in COMSOL, a two-dimensionalsimplification of the model is used, so the displacement has twocomponents: u=(u, v). The “plane strain condition” assumes that strainexists in the x-y plane, while there is no displacement in thez-direction. This assumption is not appropriate for a fluid injection ata point, but it allows for simpler design and analysis. Once asufficient model has been constructed in two dimensions, athree-dimensional model can be implemented using COMSOL's “Solid,Stress-Strain” application mode.

Values of E and v are taken from the elastic properties of soft tissue.A ranges of values is given for each parameter: 60 kPa<E<73 kPa and0.83<v<0.5. For the disclosed models, values in the middle of the rangeEγkPa and v=0.4 are used.

In FIGS. 4A-4D, the continuum model is used to estimate the fluidmovement and deformation in a 5 cm by 3 cm cross-section of tissue witha point source in the top center of this region. In order to simulate aninfiltration, fluid is made to enter the tissue at a constant rateduring times t=0 sec to t=10 sec. At t=10 sec the flow is stopped andthe tissue begins to relax. Note that the model is two-dimensional, soflow rates are expressed in units of area per time rather than volumeper time. No fluid is able to flow through the top and bottom boundarieswhich correspond to skirt and bone, respectively. Fluid is able to movethrough the side boundaries to represent flow to the rest of the body.The bottom, left, and right boundaries are unable to move, while the topboundary, representing the skin, is able to swell outwards as thepressure increases.

Specific boundary and initial conditions must be expressed for both thefluid flow and elastic deformation equations. The boundary conditionsfor equations (3.3) and (3.4) are listed in Table 3.1.

TABLE 3.1 Continuum Model Boundary Conditions Boundary Fluid FlowCondition Elastic Deformation Condition Left: n · K∇p = R_(b)(P_(b) − P)u = (0, 0) Right: n · K∇p = R_(b)(P_(b) − P) u = (0, 0) Top: n · K∇p = 0u unspecified Bottom: n · K∇p = 0 u = (0, 0)

In Table 3.1, n is the unit vector pointing outward normal to theboundary, R_(b) is the external conductance and P_(b) is the externalpressure. These conditions allow flow through the left and rightboundaries state that flow is driven by the difference in the pressurein the tissue within the model region and the pressure outside of thisregion. Since the tissue outside of the region is large in comparison tothe model domain, it is assumed that the exterior pressure stays at aconstant value, of P_(b)=0 Pa. Higher values of R_(b) correspond toeasier flow out of the region, while lower values of R_(b) result inlower flow. R_(b)=1 m⁷s/kg.

The condition u=(0, 0) stales that the displacement along the boundaryis 0, so the boundary's position is fixed. The condition where a isunspecified is called a/fee boundary condition. The initial conditionsare set to u₀=(0, 0) and p₀=0.

The model is defined in COMSOL using the parameters and boundaryconditions described in the previous section. The model is solvednumerically using an iterative method in which the pressure anddisplacement is calculated throughout the domain for many closely-spacedtime steps. The solutions to the model at times t=0 sec, t=5 sec, t=10sec, t=20 sec, t=40 sec, and t=80 sec are shown in FIG. 4D. The surfacecolor corresponds to the pressure (red represents high pressure and bluerepresents low pressure) and the changing top boundary locationcorresponds to the deformation of the tissue. As expected, the pressureis highest near the injection site and decreases at a distance from theinjection site. The solution in FIG. 4D also shows that as fluid isinjected into the tissue the region swells up and then slowly return toits original state after the infiltration is removed. This is shown inthe displacement of the top boundary condition in the solution.

The continuum model solution provides spatial quantitative informationconcerning displacements, pressures and material movement within theporous ITS which may be compared with physical measurements both in thecourse of fine-tuning a compartment model as well as in direct usewithin an instrument system.

Pressure at the injection site is plotted versus time in FIG. 4E forthree different constant injection rates: 10⁻⁷, 2·10⁻⁷, and 4·10⁻⁷ m²/s.The injection takes place between t=0 and t=10 see. The plot shows thatpressure increases monotonically during the infiltration (t=0 see tot=10 sec) and then sharply declines after the infiltration is removed(t=10 sec). The pressure decreases until reaching the value of theexternal pressure in the rest of the body. Recall that this externalpressure is specified in the side boundary conditions. Notice that thepressure does not increase linearly with time during the infiltration,but instead increases more slowly as time passes. This can be attributedto the tissue deformation. Because the volume of the tissue increases asmore fluid is injected into the region, the same influx of fluid atlater times does not increase the pressure as much, as it did initially.FIG. 4F illustrates predicted pressure at the injection site for aninjection rate of 10⁻⁷ m²/s from t=0 to t=10 sec. Time is plotted on alogarithmic scale to show an approximately straight line for timesearlier than t=10 sec. For an injection of a constant rate, the modelpredicts that the pressure at the injection site will grow according toa logarithmic function of time. FIG. 4F demonstrates that the pressuregrows approximately according to a logarithmic function of time.

FIG. 4E illustrates pressure evaluated along a line passing through theinjection site (x=0.025 meters), Plots are shown at t=5 (duringinfiltration) and at t=15 seconds (following infiltration) todemonstrate the stretching and relaxing of tissue. FIG. 4E demonstratesthe spatial variance of pressure during and shortly following aninfiltration. The pressure is evaluated along a line passing through theinjection site (x=0.025 meters) for the constant injection rate 10⁻⁷m²/s. The two plots show pressure during infiltration as t=5 and shortlyfollowing infiltration at t=15 seconds. During infiltration, there is asharp peak at the injection site, but following injection the peakquickly decreases as the fluid disperses throughout the region oftissue.

In addition to the two-dimensional fluid flow model presented in theprevious two sections, a three-dimensional axisymmetric model can beused. The axisymmetric model uses the three-dimensional equations forporoelasticity in cylindrical polar coordinates (r, φ, z) but assumesthat the variables do not vary with the angle φ. The model is thensolved in the two-dimensional r-z plane and later mapped to threedimensions. The assumption of axial symmetry reduces the complexity ofthe model compared to a full three-dimensional model, reducing thedifficulty and time of obtaining a solution.

FIG. 4H illustrates an axisymmetric model in the two-dimensional r-zplane. The solution is shown at t=50 seconds for an injection of fixedpressure 100 Pa from t=0 to t=10 seconds.

An example of a solution to the axisymmetric model is shown in FIG. 4I,which illustrates the axisymmetric model mapped from the two-dimensionalr-z plane to three dimensions. The solution is shown at t=50 seconds foran injections of fixed pressure 100 Pa from t=0 to t=10 seconds. Theaxisymmetric model uses the same parameter values boundary conditions asthe two-dimensional models shown in earlier sections, with the exceptionthat, instead of a flow source, a pressure source of 100 Pa is used atthe center of the region.

Flow sources are not implemented at the symmetry axis r=0 because of themanner in which COMSOL treats flow sources in an axisymmetric domain.

In comparing the compartment model with the continuum model, the threecompartment model tracks fluid volume and protein mass in threecompartments: the vein (plasma), the interstitial tissue near theinfiltration site, and the remainder of the body tissue. Fluid volumesin the tissue compartments are important because volume increasesreflect deformation of the tissue and serve as primary indicator ofinfiltration into the interstitial space. Protein mass influences therate of change of volume between the three compartments, since differentprotein concentrations add to the osmotic gradient and drive fluid flow.In contrast, the continuum model provides the total deformation of eachcompartment and distribution of fluid throughout the body, but not thedistribution of fluid or mass within each compartment.

In contrast, the continuum model shows, distribution of fluid andpressure in a single compartment but does not incorporate flow betweencompartments. No lymph or capillary activity is present in the presentedform of the continuum model though this may be accomplished by additionof an array of flow ‘sinks’ dispersed throughout a three dimensionalmodel space. Here, flow due to pressure gradients or flux out of acompartment is seen.

The approaches complement each other since the compartment modelsimulates flow between distinct regions and the continuum modelsimulates flow within a region. The two models can be compared by usinga compliance relationship to calculate pressure from volume in thecompartment model. This gives continuous pressure output for both modelsthat can be compared for identical inputs. Additionally, both modelspredict the expected increase in volume for a given fluid input. In thismanner, they could both be used to predict the maximum flow rate abovewhich infiltration will be harmful to a patient.

The three-compartment can be modified to reflect more realisticurination modeling, further sensitivity analysis, and parameterestimation for neonates and elderly patients. It can be further extendedto a larger number of compartments if needed to provide higherresolution.

In certain embodiments, in the three-compartment model fluid loss fromthe body (urination and perspiration) and fluid input to the body(ingestion, infusion, and infiltration) is described in constant terms.Therefore, in order for the system to reach a steady state volume thefluid input is defined as equal to the fluid loss. This is realistic fordescribing the steady stare volume, but might be unrealistic duringinfiltration events because the body adjusts urination to maintainequilibrium based on the venous plasma volume. When fluid is beinginfused directly into the tissue, less fluid enters the plasma and thevenous plasma volume drops. Consequently, the urination rate shoulddecrease as well. In certain embodiments, the urination rate could bemodeled as a constant (a) plus a term proportional to the differencefrom normal plasma volume, i.e.

J _(w)=α+β(V _(PL) −V _(PL) ₀ )

In certain embodiments, the disclosed model currently predicts theresponse to infiltrations of different flow rates and durations foradults. Parameters can be adjusted in order to predict the response ofneonates and elderly patients to infiltrations. In certain embodiments,certain parameters may be varied if any differ most greatly betweenhealthy adults, neonates, and elderly. This is particularly pertinentbecause most infiltrations occur in neonates and elderly patients.

In certain embodiments, the accuracy of the continuum model canadjusted. In certain embodiments, although the current model takes intoaccount the increase in volume due to tissue deformation, the hydraulicconductivity is held constant. As tissue expands, the pores in thetissue become larger and allow easier flow, so in certain embodimentsthis behavior can be modeled by expressing the hydraulic conductivity asa function of tissue dilation where greater dilation, leads to largerhydraulic conductivity values. In certain embodiments, hydraulicconductivity is expressed as K=H exp(Re) where K is the hydraulicconductivity, e is the tissue dilation, and H, and R are positiveconstants.

In certain embodiments, the continuum model does not directly accountfor lymph flow. Instead, the flow out of the tissue region is assumed tobe a result of flow into the rest of the body. In certain embodiments, aflow rate out of the tissue representing the lymph flow is incorporatedthat could be based on the lymph flow relationship seen in thecompartment model. In addition, for the side boundary conditions it isassumed that the pressure in the tissue outside of the region consideredis held constant at p=0 Pa. In certain embodiments, this pressureincreases as fluid flows out of the injection region into the rest ofthe body.

In certain embodiments, the continuum model could be expanded todescribe a nonsymmetrical three-dimensional region of tissue. Thecurrent three-dimensional model describes a region of tissue with axialsymmetry. In certain embodiments, flow is modeled in a fullthree-dimensional tissue model without a convergent solution. In certainembodiments, this model may involve systematically testing differentsolvers in COMSOL and varying the finite element mesh. Obtaining asolution in a basic cube or cylindrical geometry are focused on. Inorder to model an infiltration in the arm, the region 400 shown in FIG.4A is considered. In certain embodiments, this kind of model is expandedto include different tissue types by varying parameter values indifferent regions.FIG. 5 is an exemplary process 500 for monitoring the delivery ofmedication using: the medication delivery monitoring system 100 ofFIG. 1. In certain embodiments, the process 500 of FIG. 5 is embodied inprocessor 106 as computer-readable instructions configured to be storedin memory 126 (e.g., as software), which can then be loaded onto asystem 100 or other machine as illustrated and described in FIG. 1.

The process 500 begins from step 502 and proceeds to steps 504, 506, and508 in which patient information, VAD information, and medicationinformation, respectively, are provided to the system 100. Next, in step510, medication is infused into the patient 116. The process 500proceeds to loop steps 512 to 528, which repeat as long as medication118 is infused to the patient. In certain embodiments, the system 100functions indifferently to the type of medication being infused, exceptfor the potential to adjust response thresholds when certain highlyvesicant medications, such as vincristine or adriamyacin, are beinginfused. In steps 514-516, the system 100 determines a current pressure,compliance, and resistance of the fluid delivery channel 110. In certainembodiments, other current values are determined. In step 518, a modelis generated based on the provided information (e.g., the patientinformation, VAD information, and medication information), currentpressure, and current resistance, and in step 520, a predicted modelstate of the infusion site region 114 is output. In certain embodiments,other information is output, such as an expected pressure and expectedresistance of the infusion site region 114. In step 522, the currentpressure and current resistance are processed with the predicted modelstate. If in decision step 524 the current pressure and currentresistance, as compared to the predicted model state of the infusionsite region 114 indicate an infiltration has occurred, then acommunication is output in step 526. Otherwise, the process 500 proceedsto decision step 525, in which, if it is determined that the model stateestimates and/or physical measured values exceed alarm-alert thresholdsfor the patient and VAD, then an appropriate communication is output instep 526. Otherwise, the process 500 proceeds to end loop step 528. If,in end loop step 528, the medication infusion is not complete, theprocess 500 returns to beginning loop step 512, otherwise the process500 ends in step 530.

Having set forth in FIG. 5 a process 500 for monitoring the deli very ofmedication using the medication delivery monitoring system 100 of FIG.1, an example will now be presented using the process 500 of FIG. 5 andan adult patient.

The process 500 begins from step 502 and proceeds to steps 504, 506, and508 in which the adult patient information, VAD information, andmedication information, respectively, are provided, to the system 100.Next, in step 510, medication is infused into the patient 116. Theprocess 500 proceeds to loop steps 512 to 528, which repeat as long asmedication 118 is infused to the patient. As an example in steps514-516, the system 100 measures a current pressure (which is equal tothe flow times the resistance of the field delivery channel 110 plus anyhydrostatic offset), a current resistance (which includes the sum of theVAB, connecting tubing and vessel resistance), and compliance of thedelivery channel 110. In step 518 the compartment/and-or continuummodels are employed to generate estimated states of the delivery system.In step 520 some or all of these values may be output for presentationvia the user interface. In step 522, measured physical parametersincluding resistance, compliance and pressure integrated-with output ofthe model for further decision logic operations in step 524. In certainembodiments, other current values are determined. In step 518, a modelis generated based on the provided information (e.g., the patientinformation, VAD information, and medication information and the flowhistory), current pressure, and current resistance, and in step 520, apredicted model state of the infusion site region 114 is output, such aswhether there is infused fluid in infusion site region, and possiblyprotein. In certain embodiments, other information is output, such as anexpected pressure and expected resistance of the infusion site region114. In decision step 524, the current pressure and current resistanceare processed with for predicted model state. In step 526, acommunication is output because a threshold of alarm for infiltration,as defined by a clinician as an estimated number of microliters perkilogram for an adult patient, is triggered. The medication infusion isindicated as complete in step 528, so the process 500 ends in step 530.

Another example will now be presented using the process 500 of FID. 5and a neonatal pattern. The process 500 begins born step 502 andproceeds to steps 504, 506, and 508 in which the neonatal patientinformation, VAD information, and medication information, respectively,are provided to the system 100. Next, in step 510, medication is infusedinto the patient 116. The process 500 proceeds to loop steps 512 to 528,which repeat as long as medication 118 is infused to the patient. Insteps 514-516, the system 100 determines a current pressure, a currentresistance, of 2 mmHg/liter/h plus the catheter resistance, andcompliance, a high compliance value of greater than 4 microliters/mmHg,of the fluid delivery channel 110. In certain embodiments, other currentvalues are determined. In step 518, a model is generated based on theprovided information (e.g., the patient information, VAD information,and medication information), current pressure, and current resistance,and in step 520, a predicted model state of the infusion site region 114is output, such as whether there is infused fluid in infusion siteregion, and possibly protein. In certain embodiments, other informationis output, such as an expected pressure and expected resistance of theinfusion site region 114. In step 522, the current pressure and currentresistance are processed with the predicted model state. In decisionstep 524 the current pressure and current resistance are processed withthe predicted model state and do not indicate an infiltration, but indecision step 525 the current model state estimates and/or physicalmeasured values exceed alarm-alert thresholds (as defined by a clinicianas an estimated number of microliters per kilogram for a neonatalpatient) for the patient and VAD, so a communication is output in step526. The medication infusion is indicated as complete in step aide sothe process 500 ends in step 510.

FIG. 6 is a block diagram that illustrates an exemplary computing system000 that can perform certain aspects of the present disclosure inaccordance with one configuration of the present disclosure. Computingsystem 600 may represent any one or more of system 100. The computingsystem 600 may include communications module 605 for communicatinginformation, bus 606 for communicating information between differentmodules, and processor 615 coupled with the communications module 605for processing information. Processor 615 may represent processor 106 ofFIG. 1. The system 600 is configured to be coupled to a fluid pressuresensor device 630 of sufficient resolution, accuracy and bandwidth tomeasure fluid pressure in the fluid deli very channel 110 downstream(e.g., patient side) of the pump mechanism. The system 600 is alsoconfigured to couple to a fluid pumping mechanism device 635 andassociated controlling electronic software and hardware to provide bothcontinuous and modulated flow patterns supporting measurement of fluidflow resistance.

Computing system 600 may also be coupled to devices 620 and 525. One ormore devices 620 may represent output device 108 of FIG. 1, and one ormore devices 625 may represent user interface 102 of FIG. 1. Computingsystem may 600 further include memory 616, such as a RAM, a ROM or othermemory device, coupled to bus 606, for storing information andinstructions to be executed by processor 615. Memory 616 may also beused for storing temporary variable or other intermediate informationduring execution of instructions to be executed by processor 615.Computing system 600 may farther include data storage device 617, suchas a magnetic disk or optical disk, coupled to bus 606 for storinginformation and instructions. Memory 616, data storage 617, or both mayrepresent memory 120 of FIG. 1.

The embodiments of the present disclosure provide a system formonitoring an infusion site region of a patient and for determiningstate estimates and measurements associated with the risk that theinfusion site has become infiltrated by the improper positioning of theVAD and/or the erosion of the vessel puncture site. The system mayfurther provide alarms and alerts based on the severity of the riskmeasured. The determinations are-made based at least in part on thecomparison of one or more model estimates of states of fluids and/orprotein content in the within the body with an expected value of thesestates determined at least in part from information concerning thepatient such as weight, age, IV site location and catheter, thedetermination additionally may be based on the measurement of currentvalues and rates of change of pressure and resistance to flow of theinfusion site combined such as by Boolean logic with the previouslymentioned model estimates. The plurality of expected fluid deliverystale estimates are determined using a model of the infusion siteregion, such as a compartment or continuant model implemented through afinite element computation method. If the system determines the thatrisk that an infiltration bus occurred exceeds either an alert or analarm threshold determined at least in part through computations basedon patient information including but not limited to age and/or weightand/or VAD position and/or medication, then the system outputs an alertor alarm such as an visible or audible alarm, so that an operator cantake appropriate action in response to the infiltration. The system isalso able to present the current state(s) and measures of the IVdelivery system in graphical or numerical form, such as, for example,the current climate of the IV fluid disposed outside the vein ascomputed by the model may be presented to the clinician for their ownjudgment as to risk to the patient.

Although the term “processor” is used in various places in thedescription of preferred embodiments, such term is meant to apply to oneor more devices that perform processing and is not necessarily limitedto a single device located at one location. The term “processor” mayinclude multiple processing devices located at locations separate fromeach other. A processor may be a general-purpose microprocessor, amicrocontroller, a digital signal processor (“DSP”), an applicationspecific integrated circuit (“ASIC”), a field programmable gate array(“FPGA”), a programmable logic device (“PLD”), a controller, a statemachine, gated logic, discrete hardware components, or any othersuitable device that can perform calculations or other manipulations ofinformation, A processor may also include one or more machine-readablemedia for storing software. Software shall be construed broadly to meaninstructions, data, or any combination thereof, whether referred to assoftware, firmware, middleware, microcode, hardware descriptionlanguage, or otherwise. Instructions may include code (e.g., in sourcecode format, binary code format, executable code format, or any othersuitable format of code).

Machine-readable media may include storage integrated into a processor,such as might be the case with an ASIC. Machine-readable media may alsoinclude storage external to a processor, such as a random access memory(“RAM”), a flash memory, a read-only memory (“ROM”), a programmableread-only memory (“PROM”), an erasable PROM (“EPROM”), registers, a harddisk, a removable disk, a CD-ROM, a DVD, or any other suitable storagedevice. In addition, machine-readable media may include a transmissionline or a carrier wave that encodes a data signal. Those skilled in theart will recognize how best to implement the described functionality fora processor. According to one aspect of the disclosure, amachine-readable medium is a computer-readable medium encoded or storedwith instructions and is a computing element, which defines structuraland functional interrelationships between the instructions and the restof the system, which permit the instructions' functionality to berealized. Instructions can be, for example, a computer program includingcode. A machine-readable medium may comprise one or more media.Furthermore, “medication” is not meant to be restrictive but is meant toinclude any fluids administered to a patient.

Computer program code for carrying out operations as discussed above canbe written in an object oriented programming language such as, forexample, JAVA™, Smalltalk, or C++. However, the computer program codefor carrying out operations may also be written in conventionalprocedural programming languages, such as the “C” programming language,in an interpreted scripting language, such as Perl, or in a functional(or fourth generation) programming language such as Lisp, SML, Forth, orthe like. The software may also be written to be compatible with HLA-7requirements.

It is understood that although the present disclosure has been describedin embodiments, various modifications of the illustrative embodiments,as well as additional embodiments of the disclosure, will be apparent topersons skilled in the art upon reference to this description withoutdeparting from the scope of the disclosure, as recited hi the claimsappended hereto. It is contemplated that the appended claims will coverany such modifications or embodiments as fall within the scope of thedisclosure.

1-28. (canceled)
 29. A medication delivery monitoring device comprising:a vascular access device (VAD) configured to deliver a medication to aninfusion site region of a patient; a user interface configured toreceive input information; a sensor that measures a plurality of fluidstate parameters of a fluid delivery channel through which themedication is delivered by the VAD to the infusion site region of apatient; and a processor that (i) creates a model of a state of theinfusion site region, comprising fluid state parameters of interstitialtissue at the infusion site region, based on the measured fluid stateparameters and the input information, and (ii) provides a communicationto an output device if the measured fluid state parameters at theinfusion site region are not within expected infusion site regionparameters.
 30. The device of claim 29, wherein the model of a state ofthe infusion site region comprises an uninfiltrated and infiltratedstates.
 31. The device of claim 29, wherein the input informationcomprises any of patient information, VAD information, and medicationinformation.
 32. The device of claim 31, wherein the medicationinformation comprises at least one of a chemical nature of themedication, a concentration of the medication, a rate of infusion of themedication, and a nature of at least one diluent or additive associatedwith the medication.
 33. The device of claim 31, wherein the VADinformation comprises at least one of a type of the VAD, a dimension ofthe VAD, and a location of the VAD.
 34. The device of claim 29, whereinthe fluid state parameters comprises any of pressure, resistance,capacitance, and impedance of the fluid delivery channel.
 35. The deviceof claim 34, wherein the resistance is measured based on small scalemodulations, introduced by the processor, in an average infusion rate ofthe medication.
 36. The device of claim 35, wherein the small scalemodulations are associated with resulting pressure variations in thefluid delivery channel to further measure capacitance and impedance atan input to the fluid delivery channel.
 37. The device of claim 29,wherein the sensor is an outlet pressure sensor.
 38. The device of claim29, wherein the processor records any of instantaneous liquid stateparameters, filtered fluid state parameters, and long term trends offluid state parameters.
 39. The device of claim 29, wherein the model isany of a discrete compartment model and a continuum model.
 40. Thedevice of claim 29, wherein the state of interstitial tissue comprisesany of an amount of fluid added to an interstitial space, an amount ofprotein transported, and expected pressure values.
 41. The device ofclaim 29, wherein the state of the infusion site region comprisesprotein mass in the interstitial tissue at the infusion site region. 42.The device of claim 29, wherein the output device is a displayconfigured to illustrate any of a measured and an expected fluid stateparameters throughout a time the medication is infused into the patient.43. The device of claim 29, comprising a memory configured to store ahistory of the measured fluid state parameters, wherein the model isfurther based on the history of the measured fluid state parameters. 44.A medication delivery monitoring device comprising: a vascular accessdevice (VAD) configured to deliver a medication to an infusion siteregion of a patient; a user interface configured to receive inputinformation, wherein the input information includes patient information;a sensor that measures a plurality of fluid state parameters of a fluiddelivery channel through which the medication is delivered by the VAD tothe infusion site region of a patient, wherein the fluid stateparameters comprise pressure and resistance; an output device; and aprocessor that (i) creates a model of a state of the infusion siteregion, comprising fluid state parameters of interstitial tissue at theinfusion site region, based on the measured fluid state parameters andthe input information, and (ii) provides a communication to the outputdevice if the measured fluid state parameters at the infusion siteregion are not within the model of a state of the infusion site region.45. The device of claim 44, wherein the input information furthercomprises any of VAD information and medication information.
 46. Thedevice of claim 44, wherein the fluid state parameters further compriseany of capacitance and impedance of the fluid delivery channel.
 47. Thedevice of claim 44, wherein the sensor is a pressure sensor at an outletof the fluid delivery channel.
 48. The device of claim 44, wherein thestate of the infusion site region comprises protein mass in theinterstitial tissue at the infusion site region.
 49. The device of claim44, comprising a memory configured to store a history of the measuredfluid state parameters, wherein the model is further based on thehistory of the measured fluid state parameters.